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Lorist, E. (author), Nieraeth, Zoe (author)In this survey, we discuss the definition of a (quasi)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove versions of wellknown basic properties of Banach function spaces in the setting of quasiBanach function...review 2024
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Lorist, E. (author), Nieraeth, Z. (author)We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator T in the weighted Lebesgue scale and the compactness of T in the unweighted Lebesgue scale yields compactness of T on a very general class of...journal article 2024
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de Pagter, B. (author), Ricker, Werner J. (author)Let E be a translation invariant Banach function space over an infinite compact abelian group G and M<sub>φ</sub> be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection invariant (which ensures that φ̄ is also a multiplier symbol for E). The following Fuglede type...journal article 2022
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Lorist, E. (author), Nieraeth, Zoe (author)We prove that scalarvalued sparse domination of a multilinear operator implies vectorvalued sparse domination for tuples of quasiBanach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition is characterized by the boundedness of the multisublinear HardyLittlewood maximal operator and goes...journal article 2022
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Lorist, E. (author)In this dissertation we develop vectorvalued harmonic analysis methods. Particular emphasis is put on the study of stochastic singular integral operators, which arise naturally in the study of SPDE.doctoral thesis 2021
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Nieraeth, Z. (author)The subject of this thesis is the study of the multilinear Muckenhoupt weight classes and the quantitative boundedness of operators with respect to these weights in both the scalarvalued and the vectorvalued setting. This includes the study of multisublinear HardyLittlewood maximal operators, sparse forms, and multilinear Rubio de Francia...doctoral thesis 2021
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Veraar, M.C. (author), Yaroslavtsev, I.S. (author)In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder–Davis–Gundy type inequality is obtained.book chapter 2019
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Amenta, Alex (author), Lorist, E. (author), Veraar, M.C. (author)We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove LittlewoodPaleyRubio de Franciatype estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.journal article 2019
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Lorist, E. (author), Nieraeth, Z. (author)We give an extension of Rubio de Francia’s extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an m(sub)linear operator T:Lp1(w1p1)×⋯×Lpm(wmpm)→Lp(wp) for a certain class of Muckenhoupt weights yields an extension of the operator...journal article 2019
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Lorist, E. (author)We prove the ℓ<sup>s</sup>boundedness of a family of integral operators with an operatorvalued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the ℓ<sup>s</sup>boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a...book chapter 2019
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Dirksen, S. (author)This thesis is dedicated to the study of a class of probabilistic inequalities, called Rosenthal inequalities. These inequalities provide twosided estimates for the pth moments of the sum of a sequence of independent, mean zero random variables in terms of a suitable norm on the sequence itself. Rosenthal inequalities are named after H.P....doctoral thesis 2011
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 Van Neerven, J. (author) journal article 2007